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For which of the following values of n is (100+n)/n NOT an

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For which of the following values of n is (100+n)/n NOT an [#permalink] New post 23 Jul 2012, 03:19
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A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

97% (01:18) correct 2% (00:08) wrong based on 349 sessions
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Re: For which of the following values of n is (100+n)/n NOT an [#permalink] New post 23 Jul 2012, 03:19
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SOLUTION

For which of the following values of n is (100+n)/n NOT an integer?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

\frac{100+n}{n}=\frac{100}{n}+\frac{n}{n}=\frac{100}{n}+1=\frac{100}{n}+integer.

Now, in order \frac{100}{n}+integer NOT to be an integer \frac{100}{n} must NOT be an integer, so n must NOT be a factor of 100. Hence n=3.

Answer: C.
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Re: For which of the following values of n is (100+n)/n NOT an [#permalink] New post 23 Jul 2012, 20:56
Back solve. Immediately we realize 1,2,and 5 will yield integers. Also, 103 cannot be divisible by 3 since 1 + 0 + 3 is not divisible by 3.
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Re: For which of the following values of n is (100+n)/n NOT an [#permalink] New post 24 Jul 2012, 20:41
this resolves to 100/n+1 this implies... plugging in 3 does not yield an integer.

Ans- C[/color]
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Re: For which of the following values of n is (100+n)/n NOT an [#permalink] New post 25 Jul 2012, 01:18
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100+n/n ==> 100/n + 1, thus, if 100/n is not an integer then the sum will not be Integer...Plugging in numbers.. .we see that 3 satisfies.. Also, 100=2*2*5*5..thus, if the numbers in the answers are not one of these individual numbers/product of these numbers, will be the answer.
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Re: For which of the following values of n is (100+n)/n NOT an [#permalink] New post 27 Jul 2012, 05:41
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SOLUTION

For which of the following values of n is (100+n)/n NOT an integer?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

\frac{100+n}{n}=\frac{100}{n}+\frac{n}{n}=\frac{100}{n}+1=\frac{100}{n}+integer.

Now, in order \frac{100}{n}+integer NOT to be an integer \frac{100}{n} must NOT be an integer, so n must NOT be a factor of 100. Hence n=3.

Answer: C.
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Re: For which of the following values of n is (100+n)/n NOT an [#permalink] New post 12 Apr 2013, 07:42
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At first glance it was obvious to me to eliminate A, B and E answer choices. A quick way to avoid doing much mental math from that point on was to go back to smaller numbers that I knew were divisible and then make a judgement based on that. I started with 3. I stepped back to 99, a very clear multiple of 3. Add 99+3 = 102 which is clearly...not 103. We have our answer with no long division and really nothing more than identifying a clear multiple and adding 3. This allows for a solution in under 30 seconds for me. Hope this helps your speed.
Re: For which of the following values of n is (100+n)/n NOT an   [#permalink] 12 Apr 2013, 07:42
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